First-principles derivation of vacuum surface energies from crystal structures

Abstract

Phase separation in solid state chemistry may occur following two main mechanisms. For high interfacial energy ( γ⪢0), only local concentration fluctuations are allowed. Consequently, the new phase must first nucleate before growing up to a macroscopic scale (Classical Nucleation Theory or CNT). On the other hand, for vanishing interfacial energies ( γ∼0) macroscopic concentration fluctuations have a low energetic cost, and phase separation then leads to a deeply interconnected morphology (Spinodal Decomposition or SD). Consequently, it is very challenging to predict the order of magnitude of interfacial energies from the sole knowledge of the crystalline structure. Here we present a simple algorithm allowing to evaluate the vacuum surface energies of any crystalline material using a spherical charge approximation of density functional theory (DFT) equations and ab initio ground-state atomic properties. Using this formalism, it is easily explained why materials based on strong covalent bonds (oxides) or strong hydrogen bonds (ices) are expected to follow the CNT picture and why polymeric materials or metallic alloys prefer to undergo spontaneous SD. For materials displaying complex polymorphic behavior (such as observed for ice polymorphs), it becomes possible to find which polymorph should display the lowest surface energy and also to discriminate between correct and wrong crystallographic data. Thus we show for the first time that the reported crystal structure of ice-IV is characterized by a large negative surface energy and that it should be urgently revisited using accurate neutron diffraction data. Finally, we also demonstrate that the surface energy concept remains valid even at a molecular scale, bringing strong support to one of the most crucial hypothesis of CNT.